Using the minimum and maximum degrees to bound the diameter of orientations of bridgeless graphs

The oriented diameter of an undirected graph G, denoted by diam (G(?)), is defined as the minimum diameter of any strong orientation of G. In this paper, we prove that the oriented diameter of a bridgeless C-4-free graph is at most (37n)/ (d)2(-2[d/2]]1+1) + 19. We also consider some upper bounds of diam (G(?)) in terms of girth g, minimum degree d and maximum degree A and give some upper bounds of diam(G(?)) in bridgeless (C-4, C-5)-free graphs.